Uncertainty Quantification: Theory, Implementation, and Applications

By Ralph C. Smith. 2013

1,139 citations recorded by the source corpus.

The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material. Uncertainty Quantification: Theory, Implementation, and Applications includes a large number of definitions and examples that use a suite of relatively simple models to illustrate concepts; numerous references to current and open research issues; and exercises that illustrate basic concepts and guide readers through the numerical implementation of algorithms for prototypical problems. It also features a wide range of applications, including weather and climate models, subsurface hydrology and geology models, nuclear power plant design, and models for biological phenomena, along with recent advances and topics that have appeared in the research literature within the last 15 years, including aspects of Bayesian model calibration, surrogate model development, parameter selection techniques, and global sensitivity analysis. Audience: The text is intended for advanced undergraduates, graduate students, and researchers in mathematics, statistics, operations research, computer science, biology, science, and engineering. It can be used as a textbook for one- or two-semester courses on uncertainty quantification or as a resource for researchers in a wide array of disciplines. A basic knowledge of probability, linear algebra, ordinary and partial differential equations, and introductory numerical analysis techniques is assumed. Contents: Chapter 1: Introduction; Chapter 2: Large-Scale Applications; Chapter 3: Prototypical Models; Chapter 4: Fundamentals of Probability, Random Processes, and Statistics; Chapter 5: Representation of Random Inputs; Chapter 6: Parameter Selection Techniques; Chapter 7: Frequentist Techniques for Parameter Estimation; Chapter 8: Bayesian Techniques for Parameter Estimation; Chapter 9: Uncertainty Propagation in Models; Chapter 10: Stochastic Spectral Methods; Chapter 11: Sparse Grid Quadrature and Interpolation Techniques; Chapter 12: Prediction in the Presence of Model Discrepancy; Chapter 13: Surrogate Models; Chapter 14: Local Sensitivity Analysis; Chapter 15: Global Sensitivity Analysis; Appendix A: Concepts from Functional Analysis; Bibliography; Index

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d2229a5fa0e31c9ad257baf3c9c32c5b46fba7ea

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Citations in the corpus

A Non-Stationary 1981-2012 AVHRR NDVI3g Time Series (2014, background): “The Bayesian perspective is natural for uncertainty quantification since it provides densities that can be propagated through models [68].”
Uncertainty Quantification in the Mechanical Response of Crystal Plasticity Simulations (2019, methodology): “The Bayesian inference method is a powerful but computationally expensive tool for uncertainty quantification (UQ) in the output of a mathematical model.(23) Therefore, it is not well-suited for UQ of the results of CPFE simulations which are themselves time-consuming.”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, neutral): “[278] R.”
High-Performance Kernel Machines With Implicit Distributed Optimization and Randomization (2014, background): “This leads to the so-called Gaussian process regression (Rasmussen and Williams 2006), which is widely used in statistics and computational sciences, including geostatistics (Chilès and Delfiner 2012), design of experiments (Koehler and Owen 1996), and uncertainty quantification (Smith 2013).”
A unified framework for stochastic optimization (2019, background): “& Smith, M. L. (1981), ‘Optimal maintenance models for systems subject to failureA Review’, Naval Reseach Logistics Quarterly 28(1), 47–74.”